There are presently five equity options exchanges in the United States and approximately fifty exchanges that trade in options throughout the world. Options are traded on a number of financial instruments, such as, for example, stocks, currencies, Treasury instruments, interest rates, market indices, commodities and the like.
When an options exchange opens trading each morning, or reopens trading after a trading halt in the underlying instrument during the trading day, the exchange conducts an opening "rotation" procedure to determine the opening price for each option. The opening rotation may take upwards of 45 minutes, during which time the price of the underlying instrument may change dramatically. Presently, the opening rotation consumes a significant portion of the trading day. Additionally, present methods used by options exchanges to allocate the residual imbalance in public orders to market makers at the opening often results in undesirable and inefficient allocations.
To better explain the problems associated with opening and reopening of trading in an options market, an explanation of options is in order. For the purpose of clarity, this patent will discuss United States exchange-traded equity options. However, it will be appreciated that the discussion herein also applies to (a) options on other financial instruments traded on U.S. and non-U.S. exchanges, and (b) options of all types that are traded on non-U.S. exchanges.
An equity option is a securities contract which conveys to its owner the right, but not the obligation, to buy or sell a particular stock (called the underlying) at a specific price (called the strike price) on or before a given date.
Typically, there are two basic types of options, namely, Put options and Call options. An American-style equity Call option gives its owner the right to buy 100 shares of the underlying stock at the strike price on or before a given date. An American-style equity Put option gives its owner the right to sell 100 shares of the underlying stock at the strike price on or before a given date. (In the United States, one option contract normally equals 100 shares.) For American-style options, the owner of the option can exercise the contract at any time prior to expiration. For European-style options, the option cannot be exercised until the last trading day prior to expiration.
Equity options are generally traded on United States options exchanges at any time a pricing mechanism exists for the underlying instrument, for example, approximately during the normal hours of operation of U.S. securities exchanges.
The expiration for an option contract is typically the Saturday following the third Friday of the expiration month for the particular contract. Thus, the third Friday of the month is the last trading day for all equity options expiring that month. If the owner of the option does not exercise the option prior to expiration, then the option expires thereafter giving no rights to the owner and placing no obligation on the writer. (The writer is the person who assumes, for a Call option, the obligation to sell stock, or for a Put option, the obligation to buy stock.)
Assume that PQR Corp. is a publicly traded stock which also has publicly traded options. A typical option for this stock might be a PQR October 70 Call. A PQR October 70 Call option is a contract giving the owner of the contract the right to buy 100 shares of PQR Corp. stock at $70 per share until the third Saturday in October, if the buyer chooses to exercise that right.
Generally, there are four expiration months available for each equity option. Moreover, often there are three or more strike prices available for each expiration month of each equity option. Thus, for a single stock, there will likely be at least 24 and very possibly many more options traded for a particular underlying. (It is not unusual to have 60 different options available for a single stock.) For example, for PQR Corp. the following Put option series may be traded on an options exchange:
PQR January 70 Put PA1 PQR April 70 Put PA1 PQR July 70 Put PA1 PQR January 75 Put PA1 PQR April 75 Put PA1 PQR July 75 Put PA1 PQR January 80 Put PA1 PQR April 80 Put PA1 PQR July 80 Put PA1 the underlying security price PA1 the strike price of the option PA1 the time to expiration PA1 the volatility of the underlying security PA1 the current "risk-free" interest rate. PA1 market participants' estimates of future volatility PA1 estimates of future performance of the underlying stock PA1 supply and demand of the option and of the underlying PA1 depth of market for the option PA1 I. corresponds reasonably well to a single value of implied volatility (or in the more general case, to a linked set of implied volatilities that correspond to a predetermined implied volatility skew vs. strike price relationship); PA1 II. optimizes volume (or weighted measures of volume) across all series; and PA1 III. enables options market makers to balance the variations in supply and demand of public orders in each series at prices that provide an incentive to the market makers.
. . PA2 . .
There also would be a similar number of call option series. Thus, it will be apparent that for each underlying stock, there could be dozens of option series, each of which would be differently priced. Therefore, for each underlying stock, there are many option series that must be priced when trading on an option exchange opens or reopens.
The following terms are often used by options traders. An option "type" is either a Put or Call. An option "class" consists of option contracts having the same underlying security. An option "series" consists of option contracts of the same class having the same strike price and expiration month. For example, PQR October 60 Calls constitute a series.
A premium is the price an option buyer pays for the right to buy or sell the underlying security. The premium for an option contract is usually quoted on a per share basis, e.g., PQR October 60 Call $51/4--in this example, the premium is $51/4, and so the cost of the option contract would be $525 (i.e., 100 times $51/4).
An option may be "in-the-money," "at-the-money" or "out-of-the-money." A Call option is in-the-money if the underlying stock price is above the strike price, i.e., the owner of the Call option has the right to buy stock at a price which is less than the price the owner would have to pay to buy the shares in the open market. A Put option is in-the-money if the underlying stock price is below the strike price. An option is at-the-money when it has a strike price that is approximately equal to the current market price of the underlying stock. A Call option is out-of-the-money if the underlying stock price is below the strike price. A Put option is out-of-the-money if the underlying stock price is above the strike price.
The intrinsic value of an option contract is the in-the-money portion of the option's premium. The time value of an option contract is the part of an option's total premium that exceeds its intrinsic value--it is the amount the buyer is willing to pay for an option, above its intrinsic value, in the hope that prior to expiration its value will increase because of a favorable change in the price of the underlying. Thus, the premium for an out-of-the-money option consists entirely of time value. Accordingly, the premium for an option contract (the total price of the option) is its intrinsic value plus its time value.
In unusual market conditions, it may happen that the market premium for a deep-in-the-money option is actually lower than its intrinsic value. This condition may result from inadequate liquidity in the underlying security, which induces options market makers to purchase these contracts only at discounted prices with respect to their theoretical values. (This phenomenon has no deleterious impact on the utility of the present invention.)
There are five quantifiable factors that influence an option's price. These factors are:
Using these five factors as input to a theoretical option pricing model, such as, for example, the Black-Scholes model or the Cox-Ross-Rubenstein model, one can determine the theoretical fair option value. Option traders use the theoretical option value as a pricing guide. Additionally, given the current market value of an option, one can use a theoretical option pricing model to derive the implied volatility of the underlying.
There are other non-quantifiable factors that influence an option's price, such as:
Theoretical option pricing models produce values that reflect an option's sensitivity to changes in one of the five quantifiable factors. These sensitivities are assigned Greek names, such as delta, gamma, theta, rho and vega. Delta is a measure of the rate of change in an option's theoretical value for a one-unit change in the price of the underlying security. Thus, delta is the theoretical amount by which the option price can be expected to change for a small change in the price of the underlying. As such, it provides a local measure of the equivalent position risk of an option position with respect to a position in the underlying security. Delta may be expressed as a percentage, e.g. 63% (or simply "63" with the percentage symbol implied.) Every option contract has its own unique theoretical delta determined by the five quantifiable factors described above.
Gamma is a measure of the rate of change in an option's delta for a one-unit change in the price of the underlying security. Gamma expresses how much the option's delta should theoretically change for a $1 change in the price of the underlying. Gamma is largest when the option is at-the-money. As the underlying stock's price moves away from the option's strike price (in either direction), the gamma of that option will decrease. Gamma provides a local measure of the rate of change of delta with respect to the price of the underlying.
Theta is a measure of the rate of change in an option's theoretical value for a one-unit change in time to the option's expiration date. Vega (also known as kappa) is a measure of the rate of change in an option's theoretical value for a one-unit change in the volatility of the underlying security. Rho is a measure of the rate of change in an option's theoretical value for a one-unit change in the risk-free interest rate.
Delta and gamma are the primary measures used by those who trade in options. For example, if a trader has a portfolio that has a large absolute value of delta and a large absolute value of gamma, the trader would have a big position that is very sensitive to movements in the underlying's price, and thus, the trader would have a high risk exposure.
Volatility is a measure of stock price fluctuation. Mathematically, volatility is the annualized standard deviation of a stock's daily price changes. Implied volatility is the volatility that would cause the theoretical premium value of an option to match a market premium value, given fixed values of the remaining four quantifiable factors.
It will be appreciated that trading in options is a complex matter, particularly in light of the number of different option contracts that are listed on an options exchange, their interrelationships, and their relationship with the underlying stock. Each series will have different premiums, deltas, gammas and public order supply/demand characteristics. Increasing the complexity of the situation is that options can also be traded on stock indices, such as the S&P500 index.
United States options markets are typically conducted using an "open outcry" trading method, by which competing floor brokers, representing public orders, and market makers trading for their own accounts make bids and offers on the trading floor. Typically, trading takes place in a trading pit--a specific location on the trading floor of an exchange designated for the trading of a specific option class. A market maker is an exchange member on the trading floor who buys and sells options for his or her own account and who has the responsibility of making bids and offers and maintaining a fair and orderly market. A floor broker is a trader on an exchange floor who executes trading orders for the public.
At the opening (or reopening) of an options exchange, the exchange conducts an opening rotation procedure to determine the opening price for each option. It will be appreciated that at an opening or reopening, there are a disproportionate number of public buyers and sellers represented in each series at any particular opening price. There are many series to open; presently, the opening price of each is determined in rotation. For each series, taking into account public order supply and demand, marker makers signal their bid and offering prices, which converge to an agreed opening price for that series. All public order trades that can be matched at that price are executed, and there generally will be, at this stage, a residual imbalance of non-matched orders. The opening for all series in an options class may take upwards of 45 minutes, during which time the price of the underlying instrument may change dramatically, resulting in price discrepancies across series.
When opening multiple series of options in a common underlying security, variations in public order bids and offers across the series also will produce discrepancies in opening prices with respect to the theoretical prices that would correspond to a single implied volatility across all series. For example, a large imbalance of buy orders in one particular series might cause it to open at a significantly higher implied volatility than that of other series. Imbalances between public bids and offers at the opening must be rectified by the market makers. Also, as stated above, variations in the price of the underlying security during the time required to cycle through the opening can result in further significant discrepancies in opening prices across the series. For example, if the underlying stock or index price is falling rapidly, a later-opening call that would have been in-the-money at the beginning of the opening rotation might actually be opened at a lower price than an earlier-opening call that was opened at-the-money.
On some exchanges, once a series is opened, it cannot be traded until the end of the opening rotation. Since it takes time to perform the opening rotation, regular trading in a particular series may be delayed for a significant period of time.
Thus, in summary, the present opening method used by option exchanges takes an undue amount of time and results in inconsistencies in pricing between related series.
There are additional problems related to the present opening methods used by options exchanges, such as, for example, the mechanism by which the residual imbalance in public orders is allocated to market makers. The market makers as a group have an obligation to satisfy the residual imbalance in public orders at the opening price. The present method of accomplishing this goal is a round-robin assignment of the residual contracts to each market maker. This method of assignment often results in undesirable and inefficient allocations. For example, one market maker who is short delta might like to be a buyer of options contracts and another market maker who is long may want to increase his long position. Each market maker comes to the opening with his or her own current position and his or her desired target position after the opening. No attempt is made to meet these desires in the allocation of public order residual balances. As each market maker has unique desires, the present round-robin allocation of the residual balance in public orders may not improve, and could possibly worsen, the actual position of each market maker with respect to their desired position.
Accordingly, an opening method for trading on an options exchange is needed that enables the simultaneous opening of an options market and that takes into account public order supply and demand and the consistency in pricing between various series. Most desirably, an opening method is needed that simultaneously determines an opening price for all series, where the opening price arrived at is a reasonable compromise between (a) having the opening price consistent across all series with respect to implied volatility and (b) having an opening price that caters to the variations in public order supply and demand. Further, there is a need for a method of allocation of residual public order imbalances amongst market makers at the opening that optimizes each market marker's position with respect to his or her desired position.